{
  "law": "Q(min(L,c))=min(Q(L),Q(c))",
  "proof": "For any nondecreasing Q, if L<=c then Q(L)<=Q(c), and both Q(min(L,c)) and min(Q(L),Q(c)) equal Q(L); reverse the roles when c<=L.",
  "unrounded_capacity_warning": "min(Q(L),c) is a different construction; no commutation claim follows",
  "witness": {
    "L": 12,
    "c": 11,
    "round_after_cap": 10,
    "cap_after_round_with_unrounded_c": 10,
    "cap_after_round_with_rounded_c": 10
  }
}